Practical Prescribed-Time Synchronization for Multiweighted Complex Networks

This paper investigates the practical prescribed-time (PT) synchronization and control for the multiweighted complex networks (MCNs) with or without external disturbances. First, due to the possible out of memory and practical error tolerance, we define a class of general time-varying regulatory functions for practical PT stability, which can contain many previous special forms. The classic PT regulatory function is replaced with a positive constant after the practical settling time according to the tolerant precision. Dynamical systems are proved to achieve practical PT stability at the practical settling time, which can be calculated under a given condition, then exponentially converge after this time. Both the settling time and the tolerance precision can be prescribed arbitrarily. Next, taking the external disturbances into account, both PT and practical PT stability are strictly obtained. Furthermore, practical PT synchronization of MCNs is also investigated, i.e., its synchronization error can enter to a prescribed-precision region after prescribed time surely and exponentially converge to zero. At last, numerical simulations are provided to evaluate the effectiveness of theoretical results.